Theorems · Theorem · ring theory
algebraMap.coe_zero
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A], ↑0 = 0- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- map_zeroproof · cited by 1,614
- Algebra.caststatement · cited by 58
Cited by5
Results whose statement or proof uses this declaration.
- RCLike.ofReal_zeroproof · cited by 7
- InnerProductSpace.span_gramSchmidtNormedproof · cited by 2
- NumberField.absNorm_mul_finprod_finitePlace_eq_oneproof · cited by 1
- Matrix.posSemidef_iff_isHermitian_and_spectrum_nonnegproof · cited by 0
- IsLiouville.transproof · cited by 0